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A note on essentially closed 0-distributive lattice. (English) Zbl 1180.06011
Summary: The 0-distributive lattices have been studied by P. Balasubramani et al. In this paper, we study some properties of E-complemented 0-distributive lattices and essentially closed 0-distributive lattices in terms of pseudo-complements and closed elements. A similar result was carried out by D. Keskin [Indian J. Pure Appl. Math. 33, No. 1, 81–86 (2002; Zbl 0998.16004)] for modular lattices. It is observed that 0-distributive lattices need not be modular and modular lattices need not be 0-distributive.
06D75 Other generalizations of distributive lattices
06C05 Modular lattices, Desarguesian lattices
06D15 Pseudocomplemented lattices